help-13

[west dome]

Could you show your work

[keen thunder]

I based it on the "24"

I just followed what I saw from the book

Idk if I used it right though

[west dome]

,rotate

[keen thunder]

Well

[west dome]

Can you draw a picture of the scenario?

[west dome]

Okay, this accurately labels the situation, but it might be helpful to draw it like this isntead

[keen thunder]

Hmm

[west dome]

(im drawing one sec)

(is this picture clear?)

[keen thunder]

Yes

Ooh

[west dome]

Okay, so now you have two triangles, let me label some points

You have ABD and ABC

and you have the length of the base and height for each

which means you can use tan^-1 to find the ancle CAB and the angle DAB. Do you see what would would do from here?

[keen thunder]

No 😭 I'm really sorry

I'm really Clueless, our teacher didn't teach us anything (all are modular/only in paper, so lot of things gets cut off)

[west dome]

no problem! we can work through it together

Lets draw the triangles seperately for clarity

[keen thunder]

Thank you

[west dome]

okay, any idea how to solve for $\theta'$ and/or $\theta$?

[wraith dagger]

Migillope

[west dome]

(mind the poor handwriting)

[keen thunder]

Still no 😭

Sorry

[keen thunder]

It's fine

[west dome]

You know "SOH-CAH-TOA"?

[keen thunder]

Yes

[west dome]

What does the TOA mean?

[keen thunder]

Tangent = Opposite/Adjacent?

[west dome]

right!

so, for the first triangle, $\tan(\theta') = \frac{6}{5}$, right?

[wraith dagger]

Migillope

[west dome]

because 6 is the opposite side, and 5 is the adjacent side

[keen thunder]

Yes

[west dome]

okay, and so from here you can take the inverse tangent of both sides to obtain $\theta' = tan^{-1}\left(\frac{6}{5}\right)$

Make sense?

[wraith dagger]

Migillope

[keen thunder]

Arctan= 6/5?

[keen thunder]

Sorta

[west dome]

?

if you prefer arctan

$\theta' = \arctan\left(\frac{6}{5}\right)$

its the same thing

[wraith dagger]

Migillope

[keen thunder]

0h

What's the next step

[west dome]

Do the same process for $\theta$ in the other triangle

[wraith dagger]

Migillope

[west dome]

you'll get someting like $\theta = \arctan(...)$

[wraith dagger]

Migillope

[west dome]

Following the same pattern, you should be able to do that yourself. Let me know what you get

[keen thunder]

18/5?

[west dome]

right it out fully

$\theta = ?$

[wraith dagger]

Migillope

[keen thunder]

arctan (18/5)?

[west dome]

yes, great job

so lets go back to the original picture

[keen thunder]

Mhmm

[west dome]

What is $\alpha$ in terms of $\theta$ and $\theta'$?

[wraith dagger]

Migillope

[keen thunder]

How do I find that?

[west dome]

logic

just think about it for a bit

[keen thunder]

Cross multiply?

[west dome]

with less noise

what is alpha in terms of the two thetas

[keen thunder]

Irdk 🙁

[west dome]

ok try this instead, its the same idea

if the length of the board is x, and the length of the bottom bit is y, what is the length of ?

[keen thunder]

x-y = ?

[west dome]

yes

[keen thunder]

Oh

[west dome]

the situation with the thetas and alpha is exactly the same

the entire angle is $\theta$, the bottom bit is $\theta'$, so what is $\alpha$

[wraith dagger]

Migillope

[keen thunder]

18/5 - 6/5

12/5?

[west dome]

where did your arctans go

[keen thunder]

arctan (18/5) - arctan (6/5)

= arctan (12/5)

?

[west dome]

well no, that's not how arctan works, but the first line is correct

and that's all you need, that's the answer

[keen thunder]

Thank you so much

I'll try to figure out how to subtract it

[west dome]

you don't

i mean you can put it into a calculator

you can use $\arctan(x) - \arctan(y) = \arctan \left( \frac{x-y}{1+xy} \right)$

but this is not making your answer any simpler

[keen thunder]

60/133

[west dome]

arctan (18/5) - arctan (6/5)

[keen thunder]

The answer it's asking is degrees

[wraith dagger]

Migillope

[west dome]

oh, ok. I assume you can use a calculator then

[keen thunder]

Arctan (60/133)?

[west dome]

i dont understand why you dont just put arctan (18/5) - arctan (6/5) into your calculator.

but yes

[keen thunder]

24.28° then?

Thank you so much

[west dome]

,calc tan^{-1}(60/*133)

[wraith dagger]

The following error occured while calculating:
Error: Symbol or string expected as object key (char 6)

[west dome]

how do you use this dang wolfram bot

,w solve arctan(60/133)

good lord

😡

[west dome]

yes.

,w solve arctan(60/133) * 180/pi

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Migillope#7644

[west dome]

ok there you go @keen thunder. Is your question answered?

[keen thunder]

Yes

Thank you so much

*close

.close

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[sand ether]

Hence, or otherwise, show that

[sand ether]

I feel like my approach trivialised the problem too much, which is usually a sign that I made an error or something

What I did was

I expressed $\arccos(\frac{5}{\sqrt{28}})$ in terms of $\arctan(...)$

[wraith dagger]

azeem321

[sand ether]

I then took the tangent of both sides and showed the LHS=RHS

I took a similar approach for the last part also.

Would this approach be fine in proving the last two?

[cedar kiln]

@sand ether Has your question been resolved?

[cedar kiln]

@sand ether Has your question been resolved?

[cedar kiln]

@sand ether Has your question been resolved?

[unborn summit]

What was your answer?

[unborn summit]

and how did you express arccos in terms of arctan

I don't see why the approach would be not "fine" if you get the right answer 😛

pi/3 satisfies the first part of the question

ping me if you're back @sand ether

[cedar kiln]

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[random gale]

Hello there!

[random gale]

can anyone explain to me a couple of steps that my TA wrote? I'm unable to understand how each step goes

see i dont get

the second to third step

how do i interpret that?

[cedar kiln]

@random gale Has your question been resolved?

[random gale]

<@&286206848099549185>

hope someone can help me navigate through this 👍

[frozen bronze]

sorry for the poor quality photo, but hopefully this will help

@random gale

and then the following line would be the 3rd line of working in your TA’s working

[random gale]

Ah I see

so he says that in the equation

y = a x bar + b

the a part would be xi - x bar

and the b part would be the right hand part

do you mind explaining to me though how the fourth line and fifth line shows up as well?

@frozen bronze

im very confused as to how he pulls out a positive

and why the inside term within the series is not squared

[frozen bronze]

I’m not too sure sorry! I’ve not done series in a while😳

maybe try expand out the expressions and see if they are actually equal

you might see how your TA got to line 4 (or see if they’ve made a mistake!)

[cedar kiln]

@random gale Has your question been resolved?

[cedar kiln]

@random gale Has your question been resolved?

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[cedar kiln]

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[amber shale]

I needed help on this question. So, I tried to answer my question but I don't know how to solve it. I know the surface area of a cylinder and circumference of a circle, but I don't think it's possible to make a formula out of this. How can I make a formula so I can solve this question?

[dense wing]

if you know the surface area of a cylinder, then just use that

Hint: You can get r given the base

[cedar kiln]

@amber shale Has your question been resolved?

[cedar kiln]

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[crimson sedge]

what does L represent here?

[crimson sedge]

why did 1/h move from the exp to being multiplied

im talking about the migration from the last expression in the 2nd line to the first expression in the 3rd line with L = ...

I think thats what ln does

so where did the - 1 come form

from

in L = ....

I got no clue

I do know theres easier ways to find derivates of ln(u) thoug

You can do u'/u

[obsidian coral]

I don't think that was originally an exponent. It looks like it but that area is very small

The was $$\frac{\frac{a}{b}}{h} = \frac{a}{b} \cdot \frac{1}{h}$$

[wraith dagger]

dldh06

[obsidian coral]

Based on dividing by fraction

That a/b is the numerator

[crimson sedge]

but where did -1 come from

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[atomic folio]

hii can someone explain this to me?

[atomic folio]

I dont really understand how this works

[obsidian coral]

It's saying that g(x) = f(x + 2)

So it created a column for x + 2

[atomic folio]

yes

I get that part

[obsidian coral]

Because g(x) = f(x + 2), and for instance x = -4, then it would be g(-4) and then because of the g(x) = f(x + 2) that same x value gets used in the f part so f(-4 + 2)

Then you simplify that to be f(-2)

[atomic folio]

o

so you ad them

wait

[obsidian coral]

Then using the table, you determine what f(-2) is

Wait

I might have said something backwards

[atomic folio]

Im like not getting how they got g(-4)=f(-2)=6

sorry i just started this unit

[obsidian coral]

@dire geode Can you decipher this? I might have said something completely wrong with my logic cause I thought I knew what was going on

[dire geode]

@atomic folio what's f(x)

[atomic folio]

2

f(x+2)

[dire geode]

That's not a formula for f(x). It doesn't tell me how to calculate a value given an x

[atomic folio]

o

[dire geode]

E.g. f(x) = x+10, or x^2+6

[atomic folio]

thats like all i was given

let me ss

btw this is a lesson and i was confused so i looked at the answer key for it

it didnt say anything

[obsidian coral]

This would have been helpful now

So I was right

You do what I was saying

[atomic folio]

omg

[obsidian coral]

But there's an f(x) table

To use

[atomic folio]

im now realizing how the top relates

[obsidian coral]

So because g(-4) = f(-2) and at the table at the top, the f(x) table, f(-2) = 6

Because g(x) = f(x + 2)

[atomic folio]

i feel so dumb rn

[obsidian coral]

Does that help now?

[atomic folio]

yes

thank youuuuuu

very much

.close

[cedar kiln]

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[crimson sedge]

@sudden magnet

[cedar kiln]

Please don't occupy multiple help channels.

[muted tendon]

Use Bernoulli differential equation.

[crimson sedge]

.close

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[haughty oar]

How much is the circumference?

[west dome]

can you post the full question

what is the 16cm referring to? area?

[haughty oar]

That's the only thing

[west dome]

I find that a little unbelievable. How do you know you are meant to find perimeter?

[obsidian coral]

Circumference isn't the proper term

Circumference is normally for circles

Perimeter is for other shapes

[drifting matrix]

Given the picture has a diagonal line

my guess is that the 16 cm is the length of the diagonal line

[haughty oar]

In the figure below, ABCD is a square with length AC = 16 cm. What is the perimeter of the square ABCD? ||different language||

[west dome]

ur right

[obsidian coral]

Oh look a question when you said that you posted the full and only thing

[west dome]

just for precision purposes, this does say it is a square right?

I doubt it isn't but its possible

[haughty oar]

[west dome]

can you translate the question into english

[obsidian coral]

They did

[haughty oar]

In the figure below, ABCD is a square with length AC = 16 cm. What is the perimeter of the square ABCD?

[west dome]

oh i didnt see that

[obsidian coral]

Use Pythagorean theorem, I guess, to find a side

a^2 + b^2 = c^2

[haughty oar]

Pythagorean formula = a² = b² + c²

[obsidian coral]

But because it's a square a = b

[haughty oar]

Then how to find it

...²+...²= 16 ?

[west dome]

replace a with b in the pythagorean theorem

then solve for a

should be 16^2 there

[obsidian coral]

c = 16

So then it's c^2

[haughty oar]

I don't understand at all

[obsidian coral]

c is the hypotenuse, which is 16

The formula is a^2 + b^2 = c^2

Not a^2 + b^2 = c

[haughty oar]

oh

[obsidian coral]

Now as mentioned, a = b

[haughty oar]

Ya

[obsidian coral]

Meaning that both values are the same

[haughty oar]

m y

[obsidian coral]

So you can make that a be the letter b instead

[haughty oar]

OH

Wait

hm

...²+...² = 16²

[obsidian coral]

As mentioned don't use ...

Use letters

[haughty oar]

Oh

[obsidian coral]

If the formula is a^2 + b^2 = c^2

And a = b

[haughty oar]

a²+b² = 16²

[obsidian coral]

No

[haughty oar]

eh

[obsidian coral]

If a^2 + b^2 = c^2 and a = b, then you can change that a into b

[haughty oar]

Y

[obsidian coral]

Because it's a square, all side lengths are the same

[haughty oar]

Then how to find b

[obsidian coral]

Using math?

[haughty oar]

Yes but how

[obsidian coral]

If you change that a into b, what's the equation now?

[haughty oar]

Wait

oh

Wdym

[obsidian coral]

You create a different equation when a = b

Something like this, if I said x + y = 2 and x = y, then I can say y + y =2

Because of the fact that x = y

[haughty oar]

Ya

[obsidian coral]

So a^2 + b^2 = c^2 and a = b, what is the equation you have now?

[haughty oar]

a is equal to b

ಠ_ಠ

[obsidian coral]

Yes

Refer to my example I provided

What did I do when x = y

[haughty oar]

Wait a second, I can't understand the explanation

[obsidian coral]

If x + y = 2, and x = y, then I can make that x be y

Because it's the same value

[haughty oar]

ya

[obsidian coral]

So then it's y + y = 2

[haughty oar]

ya ik

A equals b, if b 2 means a is also 2

[west dome]

dont get frustrated, you can do it!

[obsidian coral]

Yes that's right

But in this case you don't have values for a or b

[haughty oar]

Yes, it is true

And I have to find it

Wait

[obsidian coral]

You're reformatting the equation

That's what I'm trying to get you to see

With my example

If x + y = 2, and x = y, then I can make that x be y
Then it's y + y = 2

I just reformatted

Because x and y are going to be the same

[west dome]

(this is called substitution, if you have heard the term before)

[obsidian coral]

So I just replaced x with y instead

[haughty oar]

[obsidian coral]

So back to the main question, if the equation you are using is a^2 + b^2 = c^2 and a = b

[haughty oar]

8²?

[obsidian coral]

Then that means you can replace a with b

Where did 8 come from?

There's no values involved, except for 16 and that's c

[haughty oar]

[haughty oar]

y

[obsidian coral]

Because you're looking for the sides

That's why

If the equation you are using is a^2 + b^2 = c^2 and a = b
Then that means you can replace a with b
What is that new equation?

[haughty oar]

11,31²?

[obsidian coral]

How are you getting numbers?

I'm only giving you an equation that just has letters

All I'm saying for now is replace a with b

In the equation a^2 + b^2 = c^2

[haughty oar]

b² + b² = c²

b² + b² = 16²

Is it true

[obsidian coral]

Yes

That's what I wanted

So b^2 + b^2 can be simplified

[haughty oar]

ya

4²?

[obsidian coral]

Not exactly

If you have x + x, what does that simplify to?

[haughty oar]

Hm

x . 2 ?

[obsidian coral]

Combine like terms, does that ring any bells?

Not times

[haughty oar]

aa

[obsidian coral]

No

[haughty oar]

Hm

√2² ?

[obsidian coral]

If you have 2x + 3x, you can combine like terms, because they have the same base, so then that becomes 5x

[obsidian coral]

I don't understand where you are pulling numbers from

All I'm giving are letters

[haughty oar]

So?

oh

Eh wdym

a = b

b² + b²

[obsidian coral]

b² + b² = 16²

Can be simplified

[haughty oar]

Can it be b⁴

b⁴ = 16² ?

[obsidian coral]

Not b^4

[haughty oar]

b = 8√2?

[obsidian coral]

Did you just guess that value?

[haughty oar]

Yes

I guessed it before, but I guess wrong. And when I search the internet. That's the answer

Sorry because I'm so hard to understand

[obsidian coral]

b is one of the sides

[haughty oar]

Yes and the other side is also the same right?

8√2 x 4 ?

[obsidian coral]

Yes

Like that

[haughty oar]

[obsidian coral]

Also b^2 + b^2 is 2b^2

So 2b^2 = 16^2

Then you find b

And that's for one of the sides

[haughty oar]

32√2 ?

Is that true

[obsidian coral]

If that's $8 \sqrt{2} \times 4$

[wraith dagger]

dldh06

[haughty oar]

Ya

OK

Tysm

You are very helpful, but there are still 11 more questions

.close

[cedar kiln]

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[deft forum]

How to solve these type

[deft forum]

??

[hollow osprey]

#❓how-to-get-help

[deft forum]

What’s happening

[hollow osprey]

@dapper herald

[deft forum]

<@&268886789983436800>

[calm sierra]

@dapper herald pls use an unoccupied channel

[deft forum]

Thanks

[tropic oxide]

do you have access to things like taylor series

[deft forum]

I don’t think so

[tropic oxide]

okay then you'll have to slowly and painfully multiply & divide by the conjugate

something that can help make your life a bit easier is to factor out x from the whole expression prior to doing that

[deft forum]

Okay

Now how to proceed?

[drifting matrix]

The trouble point are the competing x

so you should combine those away

so they can't compete

@deft forum Does this make sense?

[deft forum]

Nope

[drifting matrix]

let's look a simpler example maybe

[deft forum]

Okay

[drifting matrix]

x*a - x

how to solve this limit x -> infinity.

[deft forum]

If a>1 infinity?

[drifting matrix]

yeah, why?

[deft forum]

Because x*a will be big

Than x

?

[drifting matrix]

yeah but there is a better way

[deft forum]

Then?

[drifting matrix]

a*x - x = x * (a - 1)

[deft forum]

X(a-1)

[drifting matrix]

yeah

[deft forum]

Ya

[drifting matrix]

you found it yourself 😄

Now it's clear

[deft forum]

Ya

[drifting matrix]

no more x that go in opposite directions

[deft forum]

But i need to make sure that a>1?

[drifting matrix]

let's apply the same statregy to the above.

[drifting matrix]

well otherwise it is just either 0 or it approaches -infinity.

[deft forum]

But in upper example a=1

Is it not?

[drifting matrix]

well

what is a*x - x = x * (a - 1) in the limit if a = 1?

[deft forum]

Is it 0?

[drifting matrix]

Is this a question?

[deft forum]

I am not sure

[drifting matrix]

what is a - 1

[deft forum]

0

[drifting matrix]

what is x * (a - 1)

[deft forum]

0

[drifting matrix]

yeah

[deft forum]

But x tends to infinity

That’s confusing

[drifting matrix]

if you multiply any number by 0 though

you get 0

[deft forum]

Oh ya

Right

Thanks

Got it

[deft forum]

Can we do this by logic that lim( (x-a)(x-b)(x-c))^1/3 is infinity

Infinity-infinity =0

[drifting matrix]

nooo

Infinity - Infinity is not definable

because it can be a lot of things

In case of x - 1/2 x you get infinity

for x - x you get 0

for x - 2 x you get minus infinity

[cedar kiln]

@deft forum Has your question been resolved?

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[coarse stream]

Help

Yo??

<@&286206848099549185>

...

[modern compass]

what is this asking for?

[coarse stream]

2 rocks are thrown

One is thrown from a 100 meters above ground

Another is thrown upwards with a velocity of 50 m/s

So we have to find the point or in this case distance

Where both rocks would meet

[modern compass]

The first rock is thrown how? straight down? horizontally?

[coarse stream]

It says vertically lmao

[modern compass]

I feel like there's a whole question and you're just giving what you think is important rather than the question as a whole

[coarse stream]

Its just a question ma friend gave me

I have no idea what the entire ques is

Its just that this is the ques

I am also very much confused

[cedar kiln]

@coarse stream Has your question been resolved?

[cedar kiln]

@coarse stream Has your question been resolved?

[dawn jetty]

write down the displacement equations for both rocks

[coarse stream]

example

[dawn jetty]

well

if a body starts falling from 0 velocity it's displacement would be x(t)=(g*t^2)/2

so do the same
set yourself the frame of reference, plug in initial values

and remember you're looking for the time that both rocks have the same displacement

[coarse stream]

aint it distance

[dawn jetty]

this is a very elementary exmaple, if you plug that into your question in this form it will not account for some params

[dawn jetty]

well

yea

displacement is distance in a way

[coarse stream]

hmm how so ive learned about water displacement

[dawn jetty]

make sure to draw a rough sketch and see whcih direction the movement is headed for each rock

[dawn jetty]

when im saying displacement im talking about x(t)=x0+v0t+(at^2)/2

[coarse stream]

hmm

[dawn jetty]

im sure you must've learned it, correct ?

[coarse stream]

formula for water displacement?

[dawn jetty]

water displacement ?

[coarse stream]

displacement

[dawn jetty]

No water displacement is not relevant here

[coarse stream]

yes displacement

[dawn jetty]

lol im lost

im talking about mechanics displacement

[coarse stream]

same here

[dawn jetty]

change in position

[coarse stream]

when do you learn that

grade?

[dawn jetty]

uhh

maybe 7th grade physics ?

depends to which extent

[coarse stream]

what extent is this

[dawn jetty]

have you not learnt it ?

[dawn jetty]

it's an elementary concept in mechanics in physics, one of the first things that are taught

[coarse stream]

i probs learnt it but forgot the exact name

[dawn jetty]

x(t)=x0+v0t+(at^2)/2
this formula should ring a bell

[coarse stream]

define it for meh please

as in like v

[dawn jetty]

like v?

[coarse stream]

is v= velocity

[dawn jetty]

hmm

it should be in your notes

otherwise Im not sure how they expect you to solve that question without the basic principles of displacement

[cedar kiln]

@coarse stream Has your question been resolved?

[lethal jackal]

I mean maybe KingArthur hasn't heard of the word "displacement" being used to describe the situation

but that doesn't mean that one can't get an intuition for it

it's literally a problem where you model where each rock is at times t

[crimson sedge]

Actually this question is a bit flawed????

a rock thrown from 100m HITS THE GROUND

Another rock is thrown upwards (at where??????)

And 'the distance where they will both meet',
'MEET'
then the answer is 0

[upper garnet]

lol

that question is in giancoli mechanics and thermodynamics part 1

let me look if I can find it

[solar grail]

ze ock

[cedar kiln]

@coarse stream Has your question been resolved?

[cedar kiln]

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[sour glacier]

Someone please help me. Where am I going my wrong?

[dire geode]

what's the original question

[sour glacier]

Sorry it is write X but in terms of A and B. The first equation is what I’m given

These are matrices

[dire geode]

Find a matrix $X$ such that $X^{-1}X = A^3BA^{-1}B^{-1} X = I$

So you know $X = B \cdot (\cdots)$ because it has to cancel $B^{-1}$. Keep unraveling

[wraith dagger]

riemann

[sour glacier]

Oh sorry just saw that

But I did that though. Is there a part where I went wrong? Thank you

Ohhh I can keep going? But that wouldn’t work because I have to stop there

[wraith dagger]

riemann

[dire geode]

Your method for X doesn't even begin with B on the left

[dire geode]

Stop where?

Once you get an answer you think is right, multiply it by $X^{-1}$ to see if you get the identity matrix

[wraith dagger]

riemann

[dire geode]

Follow this pattern

[sour glacier]

Thank you! I didn’t have B on the left because it wouldn’t cancel out

So do I have to start over? I’m not sure if you mean I can fix one of these lines

[dire geode]

You were right up until this line

Your formula for the inverse is correct. Just your method afterwards was wrong

[dire geode]

What's the next term in X after B?

[sour glacier]

Like this?

[dire geode]

Follow this pattern

[sour glacier]

Ok thanks, I’ll keep trying

[cedar kiln]

@sour glacier Has your question been resolved?

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[midnight fractal]

how do i express this expression in terms of x without trigonometric functions?

[upper garnet]

theta will be arcsin(x)

sintheta will be

x

so final answer

[midnight fractal]

i wrote it wrong 😑

[upper garnet]

1/2((arcsin(x)-x/2))

[midnight fractal]

i have to write it without trig functions

so no arcsin in the final answer

[upper garnet]

your integral is wrong

it should be

(-sin(2theta)-2x) /4

or (-2cossintheta-2x)/4= (-1/2)*(x+cossintheta)

so (-1/2)*(arcsin+cox)

or (-1/2)*((arcsinx+xsqrt(1-x^2))

[midnight fractal]

can u draw it 😳

this is not clicking

i’m pretty certain i integrated both 1 and -cos(2θ) correctly

[cedar kiln]

@midnight fractal Has your question been resolved?

[stone owl]

.close

[cedar kiln]

@midnight fractal Has your question been resolved?

[cedar kiln]

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[mighty mortar]

Read #❓how-to-get-help

Or, if that's too much to ask,

• Don’t ask permission to ask a question, or ask if anyone knows how to solve a type of problem. Just ask your question.

Can you take a screenshot and post it here?

I think you're using a chromebook, you can screenshot by using CTRL + SHIFT + "Show Windows Key"

Here's whaat the show windows key looks like:

but

based on what i can see

i see "Guess and Check" in the top left, i feel like you just use each of the four answers and check if it's correct

[fallen heath]

<@&268886789983436800> Assessment Test

[calm sierra]

ty

[fallen heath]

Ty

[calm sierra]

.close

[cedar kiln]

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[cedar kiln]

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[tidal needle]

homework assignment that im not sure how to do

<@&286206848099549185>

should i ask in a different channel?

[cedar kiln]

@tidal needle Has your question been resolved?

[dire geode]

there's like 8 questions. pick one to start on and show your attempt

[cedar kiln]

@tidal needle Has your question been resolved?

[cedar kiln]

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[wispy harbor]

I’m not sure what I’m supposed to actually do to solve the problem, I’ve tried treating it as a polynomial but obviously it’s not. There’s no solving for x, I can’t simplify. I’m not sure what to do

[gaunt hamlet]

Use the distributive property to expand the parentheses

[wispy harbor]

Yeah apply -2 to 3x gets me -6 and 18

[glad kestrel]

not -6

somethin should be next to that

[wispy harbor]

Next to what?

[glad kestrel]

the -6

-2*3x isn't -6

[wispy harbor]

Thats what my calculator says

[gaunt hamlet]

-2*3 is -6, but you don't just have -2*3. You have -2*3x. There's an x in there

[wispy harbor]

My calculator can’t do variables unless I know what x is unfortunately

[gaunt hamlet]

You don't need a calculator. What's -2 * 3 * x?

[wispy harbor]

-6x

[gaunt hamlet]

Yes

That's what disappointing son was looking for

Now, what does 4x - 2(3x - 9) become after distribution?

[wispy harbor]

4x -6x 18

[gaunt hamlet]

You mean 4x - 6x + 18? You cant forget the addition sign

Anyways, what do you get after combining like terms?

[wispy harbor]

I thought within the parenthesis means it’s multiplied

[gaunt hamlet]

It is

But we multiplied it out

4x - 2(3x - 9) = 4x + (-2)(3x) + (-2)(-9) = 4x - 6x + 18

[wispy harbor]

What do you mean multiplied it out?

[unborn summit]

2(3x-9) means two (3x-9)'s

so its equivalent to two 3x's, and two -9's

[gaunt hamlet]

We distributed, is what I mean

[wispy harbor]

Oh yes distribution of course

And because we distributed we don’t multiply anything within the parenthesis? We add instead

4x -6x +18

[gaunt hamlet]

Well, a(b + c) = ab + ac, so -2(3x - 9) = -6x + 18

Anyway, now we have to combine like terms

[wispy harbor]

OH I see

-2 x + 18

[gaunt hamlet]

Does that look like any of the answer choices?

[wispy harbor]

Nope

[gaunt hamlet]

Look closer. Remember that addition is commutative and that a + (-b) = a - b

[wispy harbor]

Could you explain how addition is commutative

[gaunt hamlet]

Commutative means that a + b = b + a

We can switch the order

[wispy harbor]

Why does +18 turn into a negative?

[gaunt hamlet]

It doesn't.

[wispy harbor]

Oh minus 18

[gaunt hamlet]

We have -2x + 18, and we can switch the order of addition. What do we get if we do that?

[wispy harbor]

+2X - 18

[gaunt hamlet]

No, you can't just swap the signs

That's not allowed

[wispy harbor]

You just said switch, I was assuming that’s what you meant

[gaunt hamlet]

Remember a + b = b + a. Therefore, -2x + 18 = ?

Im saying switch the order of addition

Not the signs

[wispy harbor]

Hm

+18 -2X

[gaunt hamlet]

Yes

Does that answer show up in the answer choices?

[wispy harbor]

Wait why did we do that

[gaunt hamlet]

To make it look like one of our answer choices

[wispy harbor]

AH I see, random bullshit to get closer to the answer

This has been super helpful, thank you

I just didn’t realize I had to simplify

[gaunt hamlet]

-2x + 18 and 18 - 2x are identical, but the answer choice gave the latter

[wispy harbor]

Ah yeah! I would have realized that a lot sooner but I’m not looking at the book, I’m going back and looking and solving

Thank you so much

[cedar kiln]

@wispy harbor Has your question been resolved?

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[shrewd brook]

i dont understand this

[trim axle]

That is called completing the square

You can see that the constant in both sides is b+2 and 8a

So b+2 = 8a

[shrewd brook]

ok ill do some working out and show it

[trim axle]

Then try to find another equation for b

Cool

[shrewd brook]

no, ive got nothign

[trim axle]

Think about completing the square

You always put b/2 in the brackets

Because (a+x)^2 = a^2 + 2ax + x^2

So 2b/2 = a

[regal elk]

does a=b

oh waiiit

3((x+1/3b)+1/9b^2+8a

how do i turn this into a tekkit equation

$$ 3((x+1/3b)+1/9b^2+8a$$

[wraith dagger]

ShadoeStorm

[regal elk]

sick

$$ 3((x+\frac{1}{3b})+\frac{1}{9b^2} +8a$$

[wraith dagger]

ShadoeStorm

[regal elk]

whats wrong with the brackets

[cedar kiln]

@shrewd brook Has your question been resolved?

[cedar kiln]

@shrewd brook Has your question been resolved?

[cedar kiln]

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[fair narwhal]

guys does anyone know a proof for: if AxB = BxA, then A = B?

[graceful karma]

7 * 3 = 3 * 7

7 ≠ 3

[tight herald]

^

[fair narwhal]

my bad i worded it poorly

[graceful karma]

Or do you mean cross product

[tight herald]

What did you mean to say then?

[fair narwhal]

yea for 2 sets

umm does anyone know? xD

[tight herald]

?

[fair narwhal]

this for 2 sets A, B

[tight herald]

With vectors?

[gaunt hamlet]

Is that the same thing as the Cartesian product?

[drifting matrix]

I think you mean the carthesion product, not the cross product of vectors

[fair narwhal]

oh yeah im dumb sorry guys

[tight herald]

Oh lol kk

[fair narwhal]

i meant the cartesian product

[drifting matrix]

A and B are sets

[graceful karma]

Theyre set for life

[hollow osprey]

something like the cartesian product produces a set of ORDERED pairs, and the only way the ordered pairs can be the same is if the sets are the same.

[fair narwhal]

but does that suffice as proof?

[hollow osprey]

no

[fair narwhal]

...

then i got it wrong

[hollow osprey]

that's the intuition tho

[drifting matrix]

You should start eith the definition of the carthesion product

$$A \times B = { (x,y) | x \in A, y \in B }$$

[wraith dagger]

M8732

[fair narwhal]

right

is a chain of equations possible?

[drifting matrix]

btw the statement is wrong.

it's not true in general if either A or B is empty set

[hollow osprey]

this theorem might be helpful

[hollow osprey]

😮

[fair narwhal]

wait

[hollow osprey]

hes right b/c the condition to be in the set would never be true

[fair narwhal]

OK actually true

[hollow osprey]

hence cartesian product with empty set would be the empty set

[drifting matrix]

So we would need some precondition

[hollow osprey]

yeah

that neither A or B is the empty set

[fair narwhal]

Ok but i think thats already counted in though

[hollow osprey]

as m8732 showed a proof by counterexample

[fair narwhal]

wait

if A and B are empty sets its not okay or what

[drifting matrix]

Can you show the full task description?

[fair narwhal]

its in german though

[drifting matrix]

I happen to be german so that's fine for me

[drifting matrix]

yeah I would say that is just a flawed task

[fair narwhal]

wait i kinda dont get it

[drifting matrix]

A = {} and B = {9}

[fair narwhal]

so there is a case in which this isnt true

[drifting matrix]

it's wrong right

[fair narwhal]

either when A or B is empty

[drifting matrix]

A x B = B x A but not A = B

[fair narwhal]

but the set would be just a number

and not a tuple right?

[drifting matrix]

A and B can be any set

A single number, empty, all reals, whatever

[fair narwhal]

Ok

yea true actually

i get it now

because A x B = { 9 } and B x A = { 9 } too

[drifting matrix]

No no

[fair narwhal]

what

[drifting matrix]

A x B = {}

since there is no possible cjoice for one of the coordinates

like A and B are any set

but A x B is gonna be pairs

[fair narwhal]

right

[drifting matrix]

but there is no way to make a pair

because A is emoty

[fair narwhal]

right!

ok i understand now

its like if you try to draw it on the coordinate system but the x is missing

so you cant draw nothing, not even the 9

[drifting matrix]

yeah

[fair narwhal]

so it should be "nicht-leere mengen"

[drifting matrix]

yes

another way to see it is that

AxB always has as many elements as the number in A times the number in B.

[fair narwhal]

wait how did i never notice

[drifting matrix]

well if you draw it in a coordinate system

then that's just the formula for the area ofd the rectangle

[fair narwhal]

Ok

but lets say this isnt flawed

i should use that what Yottachad sent?

[drifting matrix]

For example if A = {1,2} and B={a,b,c} then AxB = {(1,a), (1,b), (1,c), (2,a), (2,b), (2,c)}

i.e. 2 *3 elements, 6

[fair narwhal]

yep

[drifting matrix]

yes

[fair narwhal]

alright thanks for your help guys

[drifting matrix]

One more hint maybe

take one element from A and show that it is in B.

and the other way around (though tha is the same argument actually)

if you show for all x in A that x in B (and the other way around) then A = B. @fair narwhal

[fair narwhal]

Okay I'll try, thank u

.close

[cedar kiln]

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[west dome]

contrapositive would also be very easy here

[cedar kiln]

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[bronze belfry]

What property of M will ensure that B is symmetric?
B(v,w) = v^TMw is symmetric if and only if the associated matrix M is symmetric.
Why does Matrix M have to be symmetric for B to be symmetric

[cedar kiln]

@bronze belfry Has your question been resolved?

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[maiden citrus]

Sorry just wanted to double check with someone for the formula f(x+h) plugging in 2x would result in such? Or am I making a mistake

[hollow osprey]

not sure what u r trying to do here?

cuz the limit would not result in an indeterminate form

is it the limit as h -> 0? and then where would you be getting a squared term?

[maiden citrus]

Sorry yes h approaching 0

Is limit

[hollow osprey]

so you did it wrong for f(x+h)

all you have to do is replace anywhere with x with x+h

[maiden citrus]

Okay so for when f(x)=2x , the function f(x+h) = 2x^2 + h or am I still wrong

[solar grail]

if f(x)=2x
f(x+h)=2(x+h)

[cedar kiln]

@maiden citrus Has your question been resolved?

[maiden citrus]

Ohhhh yes thank you it’s been a while since I’ve had a math class

[cedar kiln]

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[graceful karma]

If the first derivative is increasing (convex up)/decreasing (convex down)

Oh I thought you meant first order derivative

[cedar kiln]

@sinful bear Has your question been resolved?

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[sweet trail]

Can anyone help me for this?

[dire geode]

try to understand the problem and let that guide what you calculate, rather than trying to calculate equations and seeing if they fit your problem. do read https://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfPlanes.aspx

[sweet trail]

Still dont get it

sorry....

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[crimson sedge]

How can dividing it by square root of var would make variance equal to 1???

[crimson sedge]

How can dividing it by square root of var would make variance equal to 1???

[jaunty mural]

recall what happens to the variance when multiplying a RV by a constant.

There is a formula.

[crimson sedge]

RV?

random variable u mean?

[jaunty mural]

yes

[crimson sedge]

but this book hasn't introduced the concept of random variable yet

[jaunty mural]

no comment, then.

[crimson sedge]

suppose if the individual payoff of a game is multiplied by constant d, then expected value of this new game becomes d*Eo.. right?

[crimson sedge]

help me get out of this .. kinda stuck since mrng

[crimson sedge]

when we subtract the original expected value from each individual payoff, then the new expected value gets zero.. i got up to this. then what happens?

[jaunty mural]

??????

I dont know how to answer.

As I said, since you aren't doing RVs apparently.

[crimson sedge]

but so far i know, rv is the occurence of any event right tho' they haven't introduced the concept of random variable yet

[jaunty mural]

Please stop pinging

If I dont know something, I dont. You appear to be doing something else other than what I thought it was

[crimson sedge]

okay, i didn't see that..

[cedar kiln]

@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

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[leaden crater]

where did the 2020/2019 come from

[proven fable]

Lad it's the infinite gp formula

[leaden crater]

how do u get 2020/2019 from that

[halcyon eagle]

you guys know this? tf

so complicated holy

[leaden crater]

<@&286206848099549185>

[dire geode]

Geometric progression/series

[leaden crater]

i dont get it man

ah wait i think i see

ok ty

.close

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[crimson sedge]

\int (logx^(2))/(x)

[fallen heath]

I saw nothing (@_@;)

$\int \frac{\ln x^2}{x} \dd{x}$ ?

[wraith dagger]

Ansh

[hasty pelican]

Is it ln^2(x) or ln(x^2)?

[crimson sedge]

ln(x^2)

[cedar kiln]

@crimson sedge Has your question been resolved?

[dense hornet]

what have you tried?

[cedar kiln]

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[robust notch]

Hello! Is my answer correct? It’s on the yellow paper, the circled ones

[robust notch]

Are my answers*

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[lusty briar]

does anyone have the answer to this?

oh wait

my question was answered

apologies

[dusty hazel]

.close

[lusty briar]

.close

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[gaunt hamlet]

How do you find the maximum of a function?

[mossy bone]

With the derivative

[gaunt hamlet]

Then take the derivative

[mossy bone]

Finding where f'(x)=0

[gaunt hamlet]

Apply that to this problem

[mossy bone]

Ok

Should I use the integral or not?

[gaunt hamlet]

You have to. The function is the integral itself

You're maximizing A(a)

[mossy bone]

I know but im stuck in solving that integral

[gaunt hamlet]

You don't have to. In fact, I don't think you can

Use the FTC

[mossy bone]

OH RIGHT

hahaha

Haven't thought about that

thanks

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[mossy bone]

.reopen

[cedar kiln]

✅

[mossy bone]

.close

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[crimson sedge]

How can I start

[south tundra]

Try factoring x^2 - 20x - 1

[crimson sedge]

Ok

I can’t factor it